Delocalization process, communal entropy and assimilation

The concept of communal entropy has featured within the lattice models of liquids and mixtures. We show in this appendix that this entropy change is due to a combination of assimilation and expansion. 

In figure J.l, we depict a process of delocalization. Initially, we have N particles each confined to a cell of size v. We remove all the partitions and the particles are allowed to occupy the entire volume V. The entropy change upon the removal of all the partitions is 

This is known as the communal entropy. Closer examination reveals that AS in equation (J.2) is a net result of two effects the increase of the accessible volume 

Note that since we chose v = V/N, the first term on the rhs is the dominating one, i.e., the contribution of the volume change accessible to each particle is larger than the assimilation contribution (the latter is always negative). 

Within the Stirling approximation, we have partial cancellation leading to 

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